I recently had a similar issue. Mine actually got worse when something flew up off the road and impacted the pipe that extends from the sheet metal covering. The pipe was not damaged at all, but I was getting a leak only from the gray tank and not the black. Upon removing the dump valve I discovered the problem. The fitting that attaches to the gate valve and slips into the gray/black tank Waste tank slip-in adaptor 0310107  - $6.95 : Out-of-Doors Mart!, More Airstream Parts on-line than anyone!
had been over tightened at the factory. If you look at the picture below you can see that the bump had caused the final two spots of plastic to let loose. Note that the rest of the ring is discolored from a long term leak and there are two small patches of white plastic where the new break occurred. Since the replacement part is less than $7 and the work required to gain access to the area is such a pain in the, well lets just say the whole body, I decided to replace the black tank one as well. I am sure glad I decided to to that. The sheet metal below the black tank valve was slightly rusted as if water had dripped there for some time. Note in the last picture the one taken from the black tank while still intact, has several cracks that have been there for some time as is evidenced by the discoloration throughout the material.
I can not say for sure that this is what is causing your leak, but it would stand to reason that as the tank fills, the pressure builds in the tank, causing the leak to increase in volume such that it is noticeable. Once you get into the area, if this were not the case, you would still be better off accessing other potential issues.
While this repair is not an expensive one in terms of materials,(which is odd for AS) it is one that takes quiet a bit of labor hours spent laying on your back in an awkward position reaching above your head working in a very small area filled with sharp edged sheet metal.
Have I convinced you it is fun yet? Oh yea you are working in the area of the AS most people try to avoid. there you go.. Hope this helps.